Such a tire and such a method are known from U.S. Pat. No. 6,935,391. The sealing band used there comprises a layer of foam material which is impregnated with an adhesive layer performing the sealing function. A bonding layer is applied to the adhesive layer. The bonding layer is likewise produced from an adhesive and the sealing band is attached to the inner wall surface of the tire by means of the bonding layer. In U.S. Pat. No. 3,981,342, further possibilities are described for producing or introducing a self-sealing layer in or on the inner wall of a pneumatic vehicle tire. For example, it is proposed to introduce the sealing layer between the carcass and the inner layer of the tire during the production of the tire with the inner layer consisting of a rubber mixture. Furthermore, it is proposed to produce the sealing layer from a solution that is applied by means of spraying. In a further variation, the hot sealant composition is to be applied as a strip directly on the inner circumferential surface of the tire by means of extrusion. Alternatively, a strip of the sealant composition can also be extruded in an appropriate width and thickness and subsequently be applied to the inner surface of the tire.